It's a trig problem. In cartesian coordinates your buddies boat starts at x1=0, y1=0 and at any time will have x1=2.939t, y1=4.045t. Your boat starts off at x2=83.54, y2=-8.78 and will move from there and at any time have a position of x2=7tsin(a)+83.54, y2=7tcos(a)-8.78 where x and y have units of NM, t is in hours and a is the heading in degrees.

Solving this for when x1=x2 and y1=y2, you catch him after ~10.5 hours with your boat's heading of ~314 degrees.

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